6F | Division of Fractions Study Guide

Unit 6: Expressions & Equations (Fractions) • Lessons 6.1–6.2 • Standard: 6.NOS.1

Key Vocabulary

Divide — to split into equal parts or groups. (dividir)
Fraction — a part of a whole, written as a/b (numerator over denominator). (fracción)
Whole Number — a number with no fractional part (0, 1, 2, 3...). (número entero)
Mixed Number — a number with a whole part and a fraction part (e.g., 2⅓). (número mixto)
Reciprocal — the "flip" of a fraction. The reciprocal of 2/3 is 3/2. (recíproco)
Keep-Change-Flip — the method for dividing fractions: Keep the first fraction, Change ÷ to ×, Flip the second fraction. (Mantener-Cambiar-Voltear)

Visual — How Many 1/3s Fit in 2?

2 ÷ 1/3 = ?

"How many pieces of size 1/3 fit inside 2 wholes?"

  Whole 1:  [  1/3  |  1/3  |  1/3  ]
  Whole 2:  [  1/3  |  1/3  |  1/3  ]

  Count: 3 + 3 = 6 pieces!
  So 2 ÷ 1/3 = 6

Using Keep-Change-Flip:
2 ÷ 1/3 → 2 × 3/1 = 6 ✓

Step-by-Step: Keep-Change-Flip

  1. 1 KEEP the first number (don't change it). If it's a mixed number, convert to an improper fraction first.
  2. 2 CHANGE the division sign (÷) to multiplication (×).
  3. 3 FLIP the second fraction (use its reciprocal).
  4. 4 Multiply across: numerator × numerator, denominator × denominator.
  5. 5 Simplify if needed.
Example: 3/4 ÷ 3
Keep: 3/4
Change: ÷ becomes ×
Flip: 3 becomes 1/3
3/4 × 1/3 = 3/12 = 1/4
Example with mixed number: 2⅓ ÷ 1/3
Convert: 2⅓ = 7/3
Keep: 7/3   Change: ×   Flip: 1/3 becomes 3/1
7/3 × 3/1 = 21/3 = 7

Formula Box

a/b ÷ c/d = a/b × d/c
KEEP → CHANGE → FLIP

Watch Out!

Practice Problems

Type fractions as a/b (e.g., 1/4). Type whole numbers as just a number.

1. 3/4 ÷ 3 = ?

2. 5 ÷ 1/2 = ?

3. 2⅓ ÷ 1/3 = ?

4. 4½ ÷ 3/4 = ?